There was a "Starlog" interview with Harve Bennett, where Carol's non-participation in ST III was discussed. Paraphrasing: The script was all about balance. Spock was dead. A big deal. For Kirk to get Spock back, nature's balance meant that he had to lose his own son,
and also the Enterprise.
David Marcus was shown to have secretly added the protomatter to the equation for the Genesis Effect to make it work. As project leader, Carol had to have known he did it. David's punishment for cheating meant that, he had to die. If Carol was in ST III, then she would be fated to die, too. Bibi Besch had contacted Harve Bennett to ask why she wasn't in ST III and this was what he told her.
She did get to voice a Star Trek audiobook: "Faces of Fire".
If David was always meant to be killed, then his presence in TSFS explains itself.
Saavik was the "next generation" of Starfleet, as clearly sold in TWOK, and being under the direct guidance of Spock made her a key figure, so her being on the Grissom and building a relationship with David was a natural course for the character.
When they didn't know if Nimoy was returning or not, the plan was to groom Saavik and David to be the young leads of a series of telemovies, with as many of the remaining TOS cast who wanted to keep working as possible. A small exploratory vessel, with a reversal of TOS's two leads: Kirk's son, the science officer, and Spock's daughter analog, the one in command.
As soon as Nimoy asked to direct ST III, all other plans were abandoned. ST III was to be a movie, and Spock would be back, somehow.